As a method for measuring information about the diffusion of particles, the present inventors proposed an apparatus and method described below. A pair of comb-like electrodes electrically connecting one of ends of plural electrode pieces is disposed in a container for storing therein a sample in which particles are dispersed in a medium such that the other ends of electrode pieces of respective electrodes face each other with minute intervals. A voltage is applied to the electrode pair to generate the electric field distribution arranged regularly between the electrode pieces facing each other and thereby cause a migrating force to operate on the particles in the sample in the container to generate a diffraction grating resulting from the density distribution of the particles. While the application of voltage to the electrode pair is stopped to diffuse the particles and thereby annihilate the diffraction grating after the generation of the diffraction grating, diffracted light intensity obtained by applying light to a portion of the container where the diffraction grating is generated is detected. From the temporal change of the diffracted light intensity in the annihilation process of the diffraction grating, information about the diffusion of the particles in the sample is evaluated (refer to Patent Literature 1, for example).
The present inventors demonstrated that the temporal change of diffracted light measured according to the method based on the above proposal facilitates the calculation for obtaining information such as the diffusion coefficient and/or particle size with accuracy (refer to non Patent Literature 1, for example).
That is, assuming that I represents the diffracted light intensity in the annihilation process of the diffraction grating resulting from the density distribution of particles, Io represents the starting value of the diffracted light intensity (immediately after the start of the annihilation), D represents the diffusion coefficient of the particles to be measured, and Λ represents the grating period, they are approximated by the following Expressions (A) and (B).[Mathematical Expression 1]I=I0exp(−2Dq2t)  (A)
                    [                  Mathematical          ⁢                                          ⁢          Expression          ⁢                                          ⁢          2                ]                                                            q        =                              2            ⁢                                                  ⁢            π                    Λ                                    (        B        )            
The size “d” of the particles to be measured can be obtained from the following Einstein-Stokes relational expression using the diffusion coefficient D obtained in this way from the measured value I of diffracted light intensity in the annihilation process of the diffraction grating.
                    [                  Mathematical          ⁢                                          ⁢          Expression          ⁢                                          ⁢          3                ]                                                            D        =                                            k              B                        ⁢            T                                3            ⁢                                                  ⁢            πη            ⁢                                                  ⁢            d                                              (        C        )            
In the expression (C), kB is the Boltzmann constant, T represents an absolute temperature, and “η” if represents the viscosity of the medium (liquid) having the particles to be measured dispersed therein.
Patent Literature 1: WO 2007/010639
Non Patent Literature 1: “Nanoparticle size analysis with relaxation of induced grating by dielectrophoresis” Yukihisa Wada, shinichro Totoki, Masayuki Watanabe, Naoji Moriya, Yoshio Tsunazawa, and Haruo Shimaoka, OPTICS EXPRESS, 12 Jun. 2006/vol. 14, No. 12, pp 5755-5764